214 WALDO E. COHN 



where C is present in small amount compared to the bulk competing ion or 

 ions. The distribution coefficient is usually obtained by batch equilibra- 

 tion, but it is also related directly to the position of the C peak (50 % elu- 

 tion point) in column chromatography which, in turn, is equal to that 

 point in a breakthrough curve^ where the concentration of C in the effluent 

 is half of its concentration in the influent [(C) /(C)o = 0.5]. The ratio of the 

 distribution coefficients of two substances under the same set of conditions 

 is termed the "separation factor, "^ for it is also the ratio of the distances 

 from the origin to the peaks of the two substances when eluted under that 

 set of conditions. Thus the distribution coefficients define the peak positions. 

 The breadth or sharpness of each peak is related to column length and other 

 factors (size of particles, cross-linking, rate of flow) which are independent 

 of the distribution coefficient. 



c. Nonpolar Affinity 



The contrast in character between the polar substituents and the ben- 

 zenoid matrix underlies many of the anomalies in ion-exchange behavior. 

 Whereas the distribution coefficient of a particular solute will depend to a 

 large degree upon its charge, it will also depend upon any nonpolar affinity 

 of the solute for the polystyrene matrix and for the ions attached thereto. 

 The polar attractions are influenced by pH and by complex formation, 

 which affect the sign and degree of charge; the nonpolar attraction is rela- 

 tively independent of these factors. Nonpolar affinities exhibit a greater 

 temperature dependency than the polar. Reactions involving ions will 

 conform to the principles of stoichiometry ; those depending upon nonpolar 

 attractions will not conform so exactly and will deviate from equilibria 

 based upon stoichiometric considerations alone, 



d. Rate of Reaction 



Nonpolar interactions influence the rate of reaction. In general, the rates 

 of reaction between ions where at least one is "strong" (as is the case in 

 the sulfonic and quaternary amine resins) are more rapid and less tem- 

 perature-dependent than the nonpolar or "solubihty" reactions. The effect 

 of a slow rate of reaction upon the flow rates used in column chromtography 

 is adverse; a slow rate of reaction will require a slower flow rate to achieve 

 the symmetrical bell-shaped elution curve shown by Mayer and Tompkins* 

 to depend upon equilibrium conditions. Elevated temperatures can be used 



^ A breakthrough curve is obtained when the saturation value of a given column for 

 a particular substance in a given solution is exceeded. When this occurs, the plot 

 of C (concentration in effluent) vs. volume is of a sigmoid nature^ • * and approaches 

 Co (influent concentration) as a maximum. 



8 S. W. Mayer and E. R. Tompkins, /. Am. Chem. Soc. 69, 2866 (1947). 



